If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from $2: 3$ to…

If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from $2: 3$ to $3: 4$, the efficiency of the engine changes by
  1. $25 \%$
  2. $40 \%$
  3. $50 \%$
  4. $15 \%$

Solution

For carnot engine, $\begin{aligned} & \eta_1=1-\frac{T_2}{T_1}=1-\frac{2}{3}=\frac{1}{3} \\ & \eta_2=1-\frac{T_2^{\prime}}{T_1^{\prime}}=1-\frac{3}{4}=\frac{1}{4} \\ & \% \text { change in } \eta=\frac{\eta_1-\eta_2}{\eta_1} \times 100 \\ & =\frac{\frac{1}{3}-\frac{1}{4}}{\frac{1}{3}} \times 100=25 \% \end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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